Matthew Otwinowski

Acid generation rates depend critically on the value of the physico-chemical scaling parameter δ given by eq. (5.4). The scaling parameter δ can be calculated for a wide range of physical conditions characterized by the temperature T_b at the pile surface and pile porosity, ε. The chemical properties of waste rock can be characterized by the kinetic coefficient, a, and the effective active surface area, S. The value of S depends on several factors including the total content of pyrite, pyrrhotite and other sulphur compounds, the effective value of rock porosity, rock morphology, etc. In particular, one may measure rock porosity by means of the fractal dimension of pores. We feel, however, that the complexity of elementary factors responsible for the ARD potential is so high, that one should rely on the results of simple laboratory tests. Such tests should be performed for different values of temperature and different oxygen partial pressures in order to define the scaling curve αT^q and the exponent, p, for the oxidation process. Representative samples of waste rock should be used for such tests. For the needs of a predictive model it would be sufficient to perform oxidation tests under isothermic conditions at temperature intervals of 15°C in the temperature range between 5°C and 80°C and oxygen partial pressures varying between 0.21 atm and 0.01 atm at 0.05 atm intervals. Such isothermic tests should be performed at water saturation values characteristic for waste rock piles. In this way one can produce in a relatively inexpensive way the input data sufficient for a predictive model. This approach seems to be more practical than the approach based on a more direct measurement of the effective reactive surface area, S, and fractal dimensions of pores. One has to realize that microscopic factors such as the content of different morphological forms of pyrite can vary the value of S by a factor of two. The surface areas exhibited by pyrite of different morphologies vary from 6.5x10^-3 m²/g for euhedral morphology to 1.2 x 10^-2 m²/g for subhedral/framboidal morphologies [WhJ], Variation of surface area as the function of pyrite particle size is another important microscopic factor. 

The value of heat, h, generated during the pyrite oxidation process can be different for different values of acid neutralization potential. We could not find reliable data on the heat generated by calcite dissolution or the neutralization reactions, which would modify the value of h used in this report. We do not recommend, however, to measure these quantities separately. The cumulative heat generated during the weathering process is sufficient for the predictive reaction- transport model. The heat generated can be measured in the same isothermal experiment (proposed above) as the value of cooling necessary to preserve constant temperature of the oxidation process. In this way we can keep the same number of measurable coefficients as in our scaling model in which only the effective heat of pyrite oxidation is analyzed.

We also perform a simple error analysis for the scaling coefficient δ. The relative contributions due to the variation of different measurable parameters indicate the required accuracy of experimental tests. The estimated relative variation of δ, is given by:





The above formula assumes that the exact value of D is known. Our rather lengthy analysis which we do not present here, shows that the error in q has a negligibly small effect on δ/δ^* and for this reason there are no terms proportional to Δq in eq.(5.13). 

If we assume, somewhat arbitrarily, the relative accuracy Δδ/δ should be better than 25%, then we obtain the following estimate for the accuracy of the parameters involved when q=2.1:
 

We have allowed a 10% error for the directly measured simple quantities, and a 15% error for the effective coefficient α which has to be determined from a series of results and usually varies even in waste rock from the same source. A sample of waste rock with the particle size representative for the pile should be used to determine the parameter α=aS. Usual acid/base accounting tests do not provide data necessary for a predictive model which should generate quantitative information about the effluent. 

If the indicated accuracy of the experimental data is achieved, the waste rock pile should be designed so that the condition:

We hope that the last condition can be used as a practical and simple guideline for designing waste rock piles. Better estimates can be produced by a numerical model which should use nonsymmetric boundary conditions and include convective effects. When the waste rock pile is placed on the impermeable lining, the maximum allowed value of δ will increase provided the impermeable lining does not lower the heat transport rate. The present model has to be validated by using results of available laboratory and field tests before adopting the results of this study as practical guidelines.